What is the slope of a line perpendicular to the line containing the points $(4,-7)$ and $(-5,-1)$? Express your answer as a common fraction.
The slope of the line containing $(4, -7)$ and $(-5, -1)$ is $\frac{-7 - (-1)}{4 - (-5)}=\frac{-6}{9} = -\frac{2}{3}$.  Since the other line is perpendicular to this one its slope is the negative reciprocal of $-\frac{2}{3}$, giving us $\boxed{\frac{3}{2}}$.